1. Before starting, figure out how you are going to attach the lamp to the electrical box. Usually, one has a bracket like shown in photo #4 that attaches to the electrical box with screws to which the lamp is then attached.
2. I assume that the lamp has two sockets into which you will screw the bulbs.
3. Each socket has a wire with a pair of conductors (like speaker wire) connected to it.
4. For each wire, figure out which conductor is connected to the threaded portion of the socket and which conductor is connected to the terminal at the bottom of the socket.
5. Connect the two conductors that are connected to the terminal and use a wire nut to connect them to the hot (black) wire in the electrical box.
6. Connect the two conductors that are connected to the threaded portion and use a wire nut to connect them to the neutral (white) wire in the electrical box.

-- amateur

Are the wires all singles or are they the ones that are together, like a normal lamp cord?

If they are the ones that are together (SPT), then you'll notice one of the wires is smooth (black) while the other has a ribbed/rugged side (white).

If thy're not textured but they're together then it it really doesn't matter what color of wire you attach it to (when you connect white to white and black to black is mainly for the purpose to prevent electrocution if you accidentally touch the socket, but technically, you can connect the white to the black and the black to the white and the light will work).

The issue here is, that if the wires are single conductors and you can't tell which ones belong to each socket, then you can create a short circuit if you connect them wrong.

Those sconces look quite old and their wiring may be deteriorated. You should have them examined by a qualified professional and possibly rewired before you try to install them.

I also suggest that you have the same pro install them. Without any color-coding of the sconce wires, you can't install the sconces youself safely without test gear and an understanding of how to use it.

one from each top and bottom tie those together, its because it has two bulbs thuse two wires per socket, so if they where already joined together leave them like that and one set to each of the black and white wires. Dont worry about rewiring them..........its just old lamp cord not rocket science.